The Essential Guide to ANOVA for Beginners

Having a better ability to grasp data and have oversight of analytics is what is helping some companies reach new levels of innovation in this digital revolution. One of these methods is the Analysis of Variance, or ANOVA, which offers a statistical formula used to compare variances across averages of different groups. This is designed to study the effectiveness of certain experiments based on a set of people. ANOVA helps to compare these group averages, or means, to find out the statistical differences. Let’s take a closer look at the inner workings of Analysis of Variance.

ANOVA Terminology


Being able to work through these statistical modules requires an understanding of the terms affiliated with ANOVA. Within this analysis, there’s a dependent variable, an item, that is being measured and theorized to be impacted by independent variables. Independent variables are measured in that they may have an effect on the dependent variable in this research. Through ANOVA, a treatment group can discover a null hypothesis. This is where there is no difference between the averages, which can be accepted or rejected. There’s also an alternative hypothesis, which is a theorized difference within these means.

In ANOVA terminology, an independent variable is called a factor that impacts the dependent variable. Level denotes the different values of the independent variable that are used in an experiment. This analysis can occur within what is referred to as a fixed-factor model. Some experiments use only a discrete set of levels for factors. This could be in the case of testing three different dosages of a drug and not looking at other doses. There are also random-factor models, which draw a random value of level from all possible values of an independent variable.

One-Way vs. Two-Way ANOVA


There are two different types of ANOVA: one-way and full factorial, also known as two-way. The one-way analysis of variance is also known as single-factor or simple ANOVA. This is suitable for experiments with only one independent variable with two or more levels. For example, a dependent variable may be what month of the year there are more flowers growing in their garden. There will be 12 levels. One-way ANOVA assumes independence with the value of the dependent variable for one observation compared to others, as well as normalcy in the value of the dependent variable being distributed.

Two-way ANOVA, or full factorial ANOVA, is used when there are two or more independent variables. This can only be used in the case of a full factorial experiment, where there is the use of every possible permutation of factors. Using the garden scenario again, it could put a highlight on the month, as well as the number of daylight hours or monthly precipitation. Two-way ANOVA assumes that each sample is independent of other samples without any crossover to stray from its statistical significance. There’s also the variance in data across these different groups.

ANOVA and Data Science


ANOVA is more than just finding the mean for a significant result. It helps analysts to find out if the difference in the averages is of greater significance than a group may realize. ANOVA indirectly reveals if an independent variable is influencing the dependent variable in these models. If analysis of variance finds that a group average is not statistically significant, the result could infer that an independent variable is not as huge a factor as expected.

One common form of ANOVA has found its way into data science through spam detection in email accounts. The massive number of emails has made it difficult and resource-intensive to identify all spam in real time. ANOVA and F-statistics, the result of these experiments through analysis, are deployed correctly. It can make some game-changing moments to distribution and other structures within ANOVA.